Find factorial of N?
Answers
Answer:
Factorial (n!)
The factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n.
For n>0,
n! = 1×2×3×4×...×n
For n=0,
0! = 1
Factorial definition formula
n!=\begin{Bmatrix}1 & ,n=0 \\ \prod_{k=1}^{n}k & ,n>0\end{matrix}
Examples:
1! = 1
2! = 1×2 = 2
3! = 1×2×3 = 6
4! = 1×2×3×4 = 24
5! = 1×2×3×4×5 = 120
Recursive factorial formula
n! = n×(n-1)!
Example:
5! = 5×(5-1)! = 5×4! = 5×24 = 120
Stirling's approximation
n!\approx \sqrt{2\pi n}\cdot n^n\cdot e^{-n}
Example:
5! ≈ √2π5⋅55⋅e-5 = 118.019
Factorial table
Number
n
Factorial
n!
0 1
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800
11 3.991680x107
12 4.790016x108
13 6.227021x109
14 8.717829x1010
15 1.307674x1012
16 2.092279x1013
17 3.556874x1014
18 6.402374x1015
19 1.216451x1017
20 2.432902x1018
C program for factorial calculation
double factorial(unsigned int n)
{
double fact=1.0;
if( n > 1 )
for(unsigned int k=2; k<=n; k++)
fact = fact*k;
return fact;
}